Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

1

Neutron Resonance Reactions

Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

2

Neutron Activation Analysis

(Z,A) + n (Z, A+1)-

(Z+1, A+1)

(-delayed -ray)

Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

3

Neutron Attenuation

Neutrons

ndxI

dIt

TargetThickness “x”

nxo

teII

Similar to -attenuation. Why?

Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

4

Neutron Moderation

Show that, after elastic scattering the ratio between the final neutron energy E\ and its initial energy E is given by:

For a head-on collision:

After n s-wave collisions:

where

HW 44HW 44

2

2\

)1(

cos21

A

AA

E

E CM

2

min

\

1

1

A

A

E

E

nEEn lnln \

1

1ln

2

)1(1ln

2

\

A

A

A

A

E

E

av

Lethargy?

Lethargy?

Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

5

HW 44 HW 44 (continued)(continued)

How many collisions are needed to thermalize a 2 MeV neutron if the moderator was: 1H 2H 4He 12C 238U

Discuss the effect of the thermal motion of the moderator atoms.

Neutron Moderation

Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

6

Nuclear Fission

~200 MeV

Fission

Fusi

on

Coulomb effectSurface effect

Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

7

Nuclear Fission• B.E. per nucleon for 238U (BEU) and 119Pd (BEPd) ?• 2x119xBEPd – 238xBEU = ?? K.E. of the fragments 1011 J/g• Burning coal 105 J/g• Why not spontaneous?• Two 119Pd fragments just touching The Coulomb barrier is:

• Crude …! What if 79Zn and 159Sm? Large neutron excess, released neutrons, sharp potential edge…!

MeVMeVfm

fmMeVV 2142502.12

)46(.44.1

2

Crude!Crude!

Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

8

Nuclear Fission

• 238U (t½ = 4.5x109 y) for -decay.• 238U (t½ 1016 y) for fission.• Heavier nuclei??• Energy absorption from a neutron (for example) could form an intermediate state probably above barrier induced fission.• Height of barrier is called activation energy.

Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

9

Nuclear Fission

Liquid Drop

Shell

Act

iva

tion

Ene

rgy

(MeV

)

Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

10

Nuclear Fission

Surface Term Bs = - as A⅔

Coulomb Term BC = - aC Z(Z-1) / A⅓

3

3

4R

2

3

4ab=

1

)1(

Rb

Ra23 abR

...)1( 252

...)1( 251

Volume Term (the same)

32

31

52

51 )1( AaAZZa SC fission

47~2

A

Z

Crude: QM and original shape could be different from spherical.

Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

11

Nuclear Fission

48300

)120( 2

Extrapolation to 47 10-20 s.

Consistent with activation energy curve for A = 300.

Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

12

Nuclear Fission

235U + n93Rb + 141Cs + 2nNot unique.

Low-energy fission processes.

Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

13

Nuclear Fission

Z1 + Z2 = 92Z1 37, Z2 55A1 95, A2 140Large neutron excess

Most stable:Z=45 Z=58Prompt neutronsPrompt neutrons within 10-16 s.Number depends on nature of fragments and on incident particle energy.The average number is characteristic of the process.

Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

14

Nuclear Fission

The average number of neutrons is different, but the distribution is Gaussian.

Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

15

Delayed neutronsDelayed neutrons

Higher than Sn?

~ 1 delayed neutron per 100 fissions, but essential for control of the reactor.

Follow -decay and find the most

long-lived isotope (waste) in this

case.

Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

16

Nuclear Fission